In a Stirling engine cycle heat energy is converted into mechanical power by alternately compressing and expanding a fixed quantity of a gas or working fluid at different temperatures. More specifically, in a Stirling cycle electric power generator, a movable displacer moves reciprocally within the generator housing, transferring a pressurized working fluid, such as helium, back and forth between a low temperature contraction space and a high temperature expansion space. A gas cooler is provided adjacent to the pressure wall of the compression space to extract heat from the working fluid as it flows into the compression space. In conventional constructions the gas cooler may be in the form of an annular bundle of thin-walled tubes, the construction of which requires a large number of brazed connections. The large numbers of brazed joints, coupled with high internal working gas pressures, can lead to an increased likelihood of failure in this type of heat exchanger. Heat transfer is also limited in the tube bundle structure.